package Manticore::Num::Trig;

use strict;
use warnings;

use Math::BigRat lib => 'GMP';

# Sin, cos, first terms
# 1/0! - x^2/2! + x^4/4! - x^6/6!
sub proxCos {
  my ($steps, $x) = @_;
  my $mxsq = -$x*$x;
  my $sum = 0;
  my $fa = 1;
  for(1..$steps) {
    my $step2 = $_ * 2;
    $sum += $fa;
    $fa *= $mxsq/($step2*($step2-1))
  }
  return $sum
}

# x/1! - x^3/3! + x^5/5! - x^7/7!
sub proxSin {
  my ($steps, $x) = @_;
  my $mxsq = -$x*$x;
  my $sum = 0;
  my $fa = $x;
  for(1..$steps) {
    my $step2 = $_ * 2;
    $sum += $fa;
    $fa *= $mxsq/($step2*($step2+1))
  }
  return $sum
}


# sin,cos, first terms and round by continued fractions
# 1/0! - x^2/2! + x^4/4! - x^6/6!
sub proxCosCF {
  my ($steps, $x) = @_;
  my $round = sub { Manticore::Num::ContinuedFraction::roundSteps($steps, $_[0]) };
  my $mxsq = $round->(-$x*$x);
  my $sum = 0;
  my $fa = 1;
  for(1..$steps) {
    my $step2 = $_ * 2;
    $sum = $round->($sum+$fa);
    $fa = $round->($fa*$mxsq/($step2*($step2-1)))
  }
  return $sum
}

# x/1! - x^3/3! + x^5/5! - x^7/7!
sub proxSinCF {
  my ($steps, $x) = @_;
  my $round = sub { Manticore::Num::ContinuedFraction::roundSteps($steps, $_[0]) };
  my $mxsq = $round->(-$x*$x);
  my $sum = 0;
  my $fa = $x;
  for(1..$steps) {
    my $step2 = $_ * 2;
    $sum = $round->($sum+$fa);
    $fa = $round->($fa*$mxsq/($step2*($step2+1)))
  }
  return $sum
}

1;